Proton-proton Cross Section at $\sqrt{s} \sim$ 30 TeV

There are both theoretical and experimental uncertainties in using data from cosmic-ray air showers to estimate hadronic cross sections above accelerator energies. We outline these problems and compare the physics used to extract the proton-proton cross section of Donnachie and Landshoff and other contemporary models. We conclude that the published cosmic-ray cross section values do not strongly constrain \sigma_{pp}^{tot} fits from lower energy accelerator data